Our relatively large event rate with the boosted \(h\rightarrow b\bar{b}\)  analysis, grants probes at large energy scales with relevant statistics. Hence, we explore the full profile of the \(p_{Th}\)  distribution through a binned log-likelihood analysis. The new physics sensitivity is presented in Fig. REF . The HL-LHC, with 3 ab\(^{-1}\)  of data, will be able to probe these new physics effects up to a scale of \(\Lambda =2.1\)  TeV for \(n=2\)  and \(\Lambda =2.7\)  TeV for \(n=3\)  at 95% CL. These results are complementary to the off-shell Higgs analyses, \(gg\rightarrow h^{*}\rightarrow ZZ\) . For the latter, assuming \(n=3\) , the limits on the new physics scale are \(\Lambda =1.1\)  TeV for the \(4\ell \)  final state and \(\Lambda =2.1\)  TeV for the \(\ell \ell \nu \nu \)  final state [1]}, [2]}.
